Binomial Theore...

Find the coefficient of $$x^{11}$$ in the expansion of $$\left(x^{3}-\dfrac{2}{x^{2}}\right)^{12}$$

Coefficient of $$\alpha $$ in the expansion of $$(\alpha +p)^{m-1}+(\alpha +p)^{m-2}(\alpha +q)^{m-3}(\alpha +q)^{2}+....(\alpha +q)^{m-1}$$ where $$\alpha \neq -q$$ and $$p\neq q$$ is: 

If the $$r^{th}$$ and the $$(r+1)^{th}$$ terms in the expansion of $$(p+q)^{n}$$ are equal, then $$\dfrac{(n+1)q}{r(p+q)}$$ is

Number of distinct terms in the expansion of $$(x+y-z)^{16}$$ is 

The number of terms in the expansion of $$(1+x)^{101}(1+x^{2}-x)^{100}$$ in power of $$x$$ is:

In the expansion of $$(1+x)^{30}$$, the sum of the coefficients of odd powers of $$x$$, is

The coefficient of $$x^{10}$$ in the expansion of $$(1+x)^{2}(1+x^{2})^{3}(1+x^{3})^{4}$$ is qual to:

The coefficient of $$x^{n}$$ in the expansion of $$\dfrac{1}{(1-x)(1-2x)(1-3x)}$$ is 

If  the $$6^{th}$$ term in the expansion of $$\left(\dfrac {1}{x^{8/3}}+x^{2}\log ^{x}_{10}\right)^{8}$$ is $$5600$$, then equals

In the expansion of $$(1+2x+3x^{2})^{10},$$ coefficient of $$x^{4}$$ is not divisible by